Difference between revisions of "2012 AIME II Problems/Problem 2"
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] |
Revision as of 15:07, 4 July 2013
Problem 2
Two geometric sequences and
have the same common ratio, with
,
, and
. Find
.
Solution
Call the common Now since the
th term of a geometric sequence with first term
and common ratio
is
we see that
But
equals
so
See Also
2012 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.